Down-left graphs and a connection to toric ideals of graphs
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918002615648256 |
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| author | Biermann, Jennifer Castellano, Beth Anne Manivel, Marcella Petrucelli, Eden Van Tuyl, Adam |
| author_facet | Biermann, Jennifer Castellano, Beth Anne Manivel, Marcella Petrucelli, Eden Van Tuyl, Adam |
| contents | We introduce a family of graphs, which we call down-left graphs, and study their combinatorial and algebraic properties. We show that members of this family are well-covered, $C_5$-free, and vertex decomposable. By applying a result of Hà-Woodroofe and Moradi--Khosh-Ahang, the (Castelnuovo-Mumford) regularity of the associated edge ideals is the induced matching number of the graph. As an application, we give a combinatorial interpretation for the regularity of the toric ideals of chordal bipartite graphs that are $(K_{3,3} \setminus e)$-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14528 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Down-left graphs and a connection to toric ideals of graphs Biermann, Jennifer Castellano, Beth Anne Manivel, Marcella Petrucelli, Eden Van Tuyl, Adam Commutative Algebra Combinatorics 13F55 (Primary) 13D02, 13H02, 14M25 (Secondary) We introduce a family of graphs, which we call down-left graphs, and study their combinatorial and algebraic properties. We show that members of this family are well-covered, $C_5$-free, and vertex decomposable. By applying a result of Hà-Woodroofe and Moradi--Khosh-Ahang, the (Castelnuovo-Mumford) regularity of the associated edge ideals is the induced matching number of the graph. As an application, we give a combinatorial interpretation for the regularity of the toric ideals of chordal bipartite graphs that are $(K_{3,3} \setminus e)$-free. |
| title | Down-left graphs and a connection to toric ideals of graphs |
| topic | Commutative Algebra Combinatorics 13F55 (Primary) 13D02, 13H02, 14M25 (Secondary) |
| url | https://arxiv.org/abs/2304.14528 |